Create a gradient dependant of distance to an object
You can do something like this with dynamic paint.  This solution does calculate proximity from the mesh, not just the center point.

The plane should be your dynamic paint canvas, the sphere (or whatever object(s)) the brush.  I suggest painting to vertices as that's easy to use in the material node setup.  On the brush object, set your paint source to "Proximity" and set a Paint Distance that gives you the gradient values you're looking for.



Then set up your material to translate the gradient into a color gradient input to a shader.  Here I've used the wetmap.